Using the continuum model for the lipid

The LipdBase class

The class rocklinc.lipid.LipdBase handles the generation of the dx files for the APBS calculations and the reading of the result into numpy.array.

To customise the lipid model, the user could redefine rocklinc.lipid.diel_model() to the desirable dielectric constant profile and rocklinc.lipid.gaussian_mixture() to the desirable charge density profile.

The binary step lipid model

The binary step lipid model is a simple continuum model that is use to describe lipid. The charge is modelled with two Gaussians with opposite magnitude and the dielectric constant is modelled as two region with different dielectric constants.

rocklinc.lipid.StepLipid.diel_model(x, thickness, diel_low, diel_high)

The dielectric constant with respect to the distance to the end of the lipid.

Parameters

  • x (float or array) – The distance to the end of the lipid tail.

  • thickness (float) – The thickness of the lipid acryl chain, which is the distance from the end of the acryl chain and the begining of the acryl chain.

  • diel_low (float) – The dielectric constant of the region of the lipid acryl chain.

  • diel_high (float) – The dielectric constant of the region of the lipid head group and solvent.

Returns

diel – The one-dimensional array of the dielectric constant.

Return type

array

rocklinc.lipid.StepLipid.gaussian_mixture(x, magnitude, neg_loc, neg_width, pos_loc, pos_width)

Charge density with respect to the distance to the end of the lipid.

This functional form is the sum of two Gaussians with opposite magnitude.

Parameters

  • x (float or array) – The distance to the end of the lipid tail.

  • magnitude (float) – The absolute magnitude of both Gaussians (e/Å^3).

  • neg_loc (float) – The position of the Gaussians with negative magnitude (Å).

  • neg_width (float) – The spread of the Gaussians with negative magnitude (Å).

  • pos_loc (float) – The position of the Gaussians with positive magnitude (Å).

  • pos_width (float) – The spread of the Gaussians with positive magnitude (Å).

Returns

charge – The one-dimensional array of the charge density.

Return type

array

The model could be used

import numpy as np
import matplotlib.pyplot as plt
from rocklinc.lipid import StepLipid, plot_dx

lipid = StepLipid([80, 80, 80], [257, 257, 257])
lipid.write_dx_input([6.22602388e-04, 18.5969598, 1.98288109,
                                 24.1998191, 1.91347013],
                      [13.80515, 2, 80])

lipid.write_apbs_input()
lipid.run_APBS()
charge, diel, esp = lipid.read_APBS()
fig = plot_dx(np.linspace(0, lipid.dim[-1].magnitude, lipid.grid[-1]), charge, diel, esp)
plt.show()

Will give a plot looks like this

_images/stepmodel.png

The new lipid model

The new lipid model is a new continuum model that is use to describe lipid. The charge is modelled with five Gaussians to reproduce the complete electrostatic potential profile generated with explicit lipid. The dielectric constant is modelled with logistic function to reproduce the smooth switching from low to high dielectric constant region.

rocklinc.lipid.CurveLipid.diel_model(x, k1, b1, k2, b2)

The dielectric constant with respect to the distance to the end of the lipid.

Parameters

  • x (float or array) – The distance to the end of the lipid tail.

  • k1 (float) – The slope of the switching from the low to the high dielectric constant region. (1/Å)

  • b1 (float) – The length of the acryl chain. (Å)

  • k2 (float) – The dielectric constant of the solvent minus the dielectric constant of the acryl chain of the lipid.

  • b2 (float) – The dielectric constant of the acryl chain of the lipid.

Returns

diel – The one-dimensional array of the dielectric constant.

Return type

array

rocklinc.lipid.CurveLipid.gaussian_mixture(x, cho_loc, cho_std, cho_mag, po4_loc, po4_std, po4_mag, GL_loc, GL_std, GL_mag, neg_loc, neg_std, neg_mag, pos_std, pos_mag)

Charge density with respect to the distance to the end of the lipid.

This functional form is the sum of two Gaussians with opposite magnitude.

Parameters

  • x (float or array) – The distance to the end of the lipid tail.

  • cho_loc (float) – The position of the Gaussians of the choline group (Å).

  • cho_std (float) – The spread of the Gaussians of the choline group (Å).

  • cho_mag (float) – The absolute magnitude of choline group (e/Å^3).

  • po4_loc (float) – The position of the Gaussians of the phosphate group (Å).

  • po4_std (float) – The spread of the Gaussians of the phosphate group (Å).

  • po4_mag (float) – The absolute magnitude of phosphate group (e/Å^3).

  • GL_loc (float) – The position of the Gaussians of the phosphate group (Å).

  • GL_std (float) – The spread of the Gaussians of the phosphate group (Å).

  • GL_mag (float) – The absolute magnitude of phosphate group (e/Å^3).

  • neg_loc (float) – The position of the Gaussians of the negative dipole of acryl chain (Å).

  • neg_std (float) – The spread of the Gaussians of negative dipole of acryl chain (Å).

  • neg_mag (float) – The absolute magnitude of negative dipole of acryl chain (e/Å^3).

  • pos_std (float) – The spread of the Gaussians with positive dipole of acryl chain (Å).

  • pos_mag (float) – The absolute magnitude of positive dipole of acryl chain (e/Å^3).

Returns

charge – The one-dimensional array of the charge density.

Return type

array

The model could be used

import numpy as np
import matplotlib.pyplot as plt
from rocklinc.lipid import CurveLipid, plot_dx

lipid = CurveLipid([80, 80, 80], [257, 257, 257])
lipid.write_dx_input([24.1998191, 1.28409182, 3.29937546e-03,
                      18.5969598, 2.41286946, 5.70594706e-03,
                      16.0770291, 2.47034776, 4.17737240e-03,
                      6.59972225, 0.90515386, 4.25321040e-04,
                      2.95472778, 1.17224618e-04],
                      [0.36626031, 18.87278382, 76.49060424, 4.83151723])

lipid.write_apbs_input()
lipid.run_APBS()
charge, diel, esp = lipid.read_APBS()
fig = plot_dx(np.linspace(0, lipid.dim[-1].magnitude, lipid.grid[-1]), charge, diel, esp)
plt.show()

Will give a plot looks like this

_images/curvemodel.png

API Reference

class rocklinc.lipid.LipdBase(dim, grid)[source]

setup the grids for the APBS calculations.

Parameters

  • dim (list) – The unitcell dimensions of the system in Å [lx, ly, lz]. The pq.Quantity array could also be used.

  • grid (list) – The number of grids in the x, y, z axis [257, 257, 257].

static diel_model(x, **kwargs)[source]

The dielectric constant with respect to the distance to the end of the lipid.

Parameters

  • x (float or array) – The distance to the end of the lipid tail.

  • **kwargs (dict) – Additional keyword arguments.

Returns

diel – The one-dimensional array of the dielectric constant.

Return type

array

static gaussian_mixture(x, **kwargs)[source]

Charge density with respect to the distance to the end of the lipid.

Parameters

  • x (float or array) – The distance to the end of the lipid tail.

  • **kwargs (dict) – Additional keyword arguments.

Returns

charge – The one-dimensional array of the charge density.

Return type

array

generate_charge(z_list, param_charge)[source]

Generate the charge density from the coordinates.

Parameters

  • z_list (array) – The one-dimensional coordinate array.

  • **kwargs (dict) – Additional keyword arguments.

Returns

charge – The one-dimensional array of the charge density.

Return type

array

generate_diel(z_list, param_diel)[source]

Generate the dielectric constant from the coordinates.

Parameters

  • z_list (array) – The one-dimensional coordinate array.

  • **kwargs (dict) – Additional keyword arguments.

Returns

diel – The one-dimensional array of the dielectric constant.

Return type

array

read_APBS()[source]

Read the APBS output.

Returns

  • charge (array) – The three-dimensional array of the charge density.

  • diel (array) – The three-dimensional array of the dielectric constant in the x direction.

  • lipid (array) – The three-dimensional array of the ESP.

read_central_ESP()[source]

Read the one-dimensional ESP along the Z-axis at the center of the x-y plane.

Returns

out_ESP – The one-dimensional ESP.

Return type

array

run_APBS(apbs_exe='/opt/local/bin/apbs', apbs_in='lipid.in')[source]

Running the APBS calculations, which is the same as

apbs lipid.in
Parameters

  • apbs_exe (str, optional) – The path to the APBS program. (/opt/local/bin/apbs)

  • apbs_in (str, optional) – The input file to the APBS program. (lipid.in)

write_apbs_input()[source]

Generate the APBS input file lipid.in and the reference qpr file ref.pqr.

The APBS calculation will use the dielx.dx, diely.dx and dielz.dx for dielectric constant and charge.dx for the charge density. The ref.pqr is a place holder and is not used in the calculation.

write_dx_input(param_charge, param_diel)[source]

Generate the dielectric constant and charge grid for APBS calculations.

generate_charge and generate_diel are used to generate the profile of the charge and dielectric constant on the one-dimensional z-axis which is then broadcast to cover the whole 3D space. The generated files are named as dielx.dx, diely.dx, dielz.dx and charge.dx.

Parameters

**kwargs (dict) – generate_charge uses the arguments from kwargs[‘charge’] and generate_diel uses the arguments from kwargs[‘diel’].